1/3 Rule?

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Okay, I like your post above enough to submit for consideration (and possible ridicule) a slice out of a multivariate spreadsheet I once concocted. In this small excerpt, we are assuming two divers, each consuming one cubic foot per minute surface equivalent, using one eighty-cubic-foot aluminum tank (sharing air), making a thirty-foot-per-minute ascent with a three-minute safety stop at fifteen feet, and draining the tank upon surfacing. A nearly-worst-case analysis.

I hope everyone caught the phrase I put in bold and realizes that rock bottom calculations and "be back on the boat with 500 PSI" are not the same plan. For example, in the first few cases on the chart, a diver doing a safety stop with no emergency complications will not have 500 PSI getting back on the boat. If you are dealing with an operator who is being really hard nosed about that rule, you have to plan accordingly.

Many people think a rock bottom ascent plan is too conservative, but in many situations it allows much more gas usage than the 500 PSI rule. The chart indicates that you should leave 130 feet with 1720 left, but that is because of the potential for having to deal with an emergency at that depth. It does not mean the dive has to be over. If you leave 130 feet with that much gas and have a trouble free ascent to 60 feet with something to see, you are now governed by the 860 rule and can hang out until then. If you then have a trouble free ascent to 30 feet and have something to see, you can hang out until you reach the 600 PSI level. If you do, you will get on the boat with less than 500 PSI, and hopefully that is OK with your boat operator.
 
Here's another Emergency gas planning example & exercise for the OP, for a dive to the Basic Open Water Limit of 18m/60 feet:

Emergency "Stressed" 28 litres/min SCR (Surface Consumption Rate, equivalent to 1 cuft/min in US/Imperial), with 18 meters (2.8 ATA) depth NDL, and with one minute stops every 3 meters/10 feet to surface [note: a one minute stop in this example is considered a 30 second hold at the present depth plus a 30 second ascent to the next depth]:

2.8 x 28 x 1 = 78.4
2.5 x 28 x 1 = 70
2.2 x 28 x 1 = 61.6
1.9 x 28 x 1 = 53.2
1.6 x 28 x 1 = 44.8
1.3 x 28 x 1 = 36.4
1.0 x 28 x 1 = 28

Sum Total: 372.4 litres gas needed to ascend to surface for an emergency contingency.

Divide the above total by the metric tank rating of the Scuba cylinder in use; for this example let's use the AL80 tank again which has a metric rating of 11 litres/bar. So 372/11 = approx 35 bar.

That's 35 bar to get you to the surface --to get yourself and sharing gas with an Out-of-Air Buddy you will need at least twice this amount: 35 x 2 = 70 bar. Therefore your Rock Bottom Reserve is an actual reading of 70 bar showing on your SPG --if there is no emergency air sharing contingency at that instant, just continue the dive normally but start a easy nominal ascent to the shallower depths between 5m and 9m. Finally, be at your 5m safety stop with your buddy with no less than 50 bar showing on the SPG.

Your usable gas for the dive is your starting pressure subtracted by the Rock Bottom Reserve --so a full AL80 tank of 200 bar minus 70 bar equals 130 bar usable. Let's use 20 bar of this 130 to get squared away in good trim & buoyancy on the descent to 18m which then leaves 110 bar usable. Now if your dive plan calls for returning to near the vicinity of your original point of entry (like a beach dive for instance), then turn the dive back around when you use half of 110 bar or 55 bar consumed. If you want an even more conservative value because of thick kelp for example, use rule-of-thirds - 1/3 of 110 is 36 bar in this instance.

So for a nominal dive with an SCR of 22 litres/min on a 11L/bar (AL80) tank, your resulting pressure SCR will be 2 bar/min [22 divided-by 11 equals 2bar/min]. Your depth in meters, which converts easily to ATA (simply divide-by-10 and add 1) becomes your multiplier depth factor for your 2bar/min pressure SCR.

18 meters depth is 2.8 ATA (divide 18 by 10 and add 1 equals 2.8); your 2bar/min SCR at depth -or Depth Consumption Rate (DCR)- now becomes 5.6 bar/min. [2.8 times 2bar/min equals 5.6 bar/min]. So 10 minutes at depth 18m on an AL80 (11L/bar) tank in nominal conditions, you would expect to consume 56bar of gas (10min times 5.6 bar/min equals 56bar) and your SPG reading to show a delta down of 56bar. . .

Okay, you splash in to start the dive with 200bar and a 70bar rock bottom. You use up 20bar on descent --initial exertion, inflating your wing etc. -so you now have 180bar with 70bar rock bottom at present depth 18m, a net usable of 110bar (180 minus 70 is 110). Finning out for 10 minutes, an easy swim looking at all the cool marine life around -- you already know by the end of this 10 minute interval that you've used up 56bar (see previous paragraph above), so you decide to turn the dive.

You should now know you have roughly 50bar of usable gas left before encroaching on your Rock Bottom Reserve, and realize that you must start a nominal ascent within the next 10 minute interval. Alright, so while turning back, you see a turtle and decide to chase it for a few minutes, huffing & puffing on your reg, until it dives down below your operational depth of 18m; because of this physical exertion you immediately check your SPG and it reads 70bar --bingo! Rock bottom has arrived so start ascending to the shallower depths . . .or if your Buddy just happens to blow his tank neck O-ring at that instant --you know you've got plenty of breathing gas margin for a controlled air-sharing Emergency ascent profile as described above. . .

Be aware that depending on environmental conditions and physical exertion (cold water, stiff current, long surface swim, heavy workload at depth etc), you may have to decide on-the-fly to reserve a greater Rock Bottom Reserve --perhaps as high or even over 100 bar (half tank) on the 11L/AL80 tank to be even more conservative.

____
Notes for American Divers using US Imperial Units:
Stressed SCR of 28 litres/min is equivalent to 1 cuft/min;
Nominal SCR of 22 litres/min is approx 0.75 cuft/min.
2 bar/min is same as 29psi/min;
5.6 bar/min is 81psi/min

Easy imperial US/metric conversions for depth & pressure, that you can do in your head:

Depth in meters multiplied by 10/3 gives depth in feet;
Feet multiplied by 3/10 gives meters.
Example: 18m(10/3) = 60' ; 60'(3/10) = 18m

Pressure bar multiplied by 3/2, and multiplied again by 10 gives pressure psi;
Pressure psi multiplied by 2/3, and divided by 10 gives pressure bar.
Ex): 200bar(3/2)(10) = 3000psi ; 3000psi(2/3)/10 = 200bar.

___
Your common counting numbers, or reference cardinal numbers, for depth in scuba are:

Imperial US (feet) by 10's:
Ex): 10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110 etc

Metric system goes by 3's:
Ex): 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33 etc

It's easier to figure out ATA (Atmospheres Absolute depth multiplier factor) with meters:
Example: 24 meters is 3.4 ATA (divide 24 by 10 and add 1); the equivalent 80 feet in US/imperial is also 3.4 ATA, but not as easy to calculate (80 divided by 33 plus 1).
 
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Why are you planning for 1 minute stops all the way from the bottom, as opposed to from 1/2 depth on up, which is my understanding of how Minimum Deco works?
 
Why are you planning for 1 minute stops all the way from the bottom, as opposed to from 1/2 depth on up, which is my understanding of how Minimum Deco works?
Easy consistent calculation for conservatism and ensuring enough gas for a slow controlled emergency air-sharing ascent --this is the New Diver sub-forum after all.

With more experience, you can use more liberal faster ascent rate values if you wish. . .
 
jdg's Surface Consumption Rate (SCR) is 1 cubic foot per minute (28 litres/min in metric) anyway, so I wanted to be sure the gas plan example had enough to cover a range of emergency air-sharing ascent rates -from a slow sane & controlled 10 feet/min (which the plan above reflects), to the recommended 30 feet/min, to an absolute max of 60 feet/min. (That's 3m/min; 9m/min; and 18m/min respectively in metric)

If for example he actually ascended faster within the above range while doing an air-sharing contingency with an out-of-gas buddy, he would at least have time and gas for a few minutes "safety stop" at 15 feet to 10 feet (5 to 3 meters) depth. . .

---------- Post added May 2nd, 2013 at 08:53 PM ----------

If dissimilar tanks are used, take one-third of the smaller tank volume after first subtracting out Rock Bottom, and then match that amount to the remaining teammate's tank by their respective metric cylinder ratings. For conservatism, figure out Rock Bottom using the teammate with the higher Surface Consumption Rate (SCR).

Example (similar to the Gas Plan post#62 above:
28 litres/min SCR, with 18 meters (2.8 ATA) depth NDL with one minute stops every 3 meters to surface:

2.8 x 28 x 1 = 78.4
2.5 x 28 x 1 = 70
2.2 x 28 x 1 = 61.6
1.9 x 28 x 1 = 53.2
1.6 x 28 x 1 = 44.8
1.3 x 28 x 1 = 36.4
1.0 x 28 x 1 = 28

Sum Total: 372.4 litres gas needed to ascend to surface for an emergency contingency.

Suppose you have two divers with different scuba tank cylinder ratings:

In a 12 litre/bar tank, 372.4 litres is 31 bar (divide 372.4 by 12); in a 15 litre/bar tank, 372.4 is 24 bar pressure.
For these two divers sharing gas in an out-of-gas contingency, multiply the respective bar pressure readings by 2 for actual Rock Bottom pressure value of each tank:

12 litre/bar tank: 62 bar (31 bar times 2); 15 litre/bar tank: 48 bar (24 bar times 2).

The 12 litre/bar tank has a starting pressure of 180 bar; subtract out Rock Bottom of 62 bar yields 118 bar usable.
The 15 litre/bar tank has a starting pressure of 150 bar; subtract out Rock Bottom of 48 bar yields 102 bar usable.

Which of the two tanks above has the smaller remaining volume of usable gas left?
12 litre/bar x 118 bar = 1416 litres
15 litre/bar x 102 bar = 1530 litres

So the 12 litre/bar tank is the smaller remaining volume, hence we apply the Rule-of-Thirds to its usable pressure of 118 bar:
118/3 = 39 bar; so 39 bar delta down or subtracted from 118 equals an actual turn pressure SPG reading of 79 bar for the teammate with the 12 litre/bar tank.

Now the Rule-of-Thirds 39 bar delta in the 12 litre/bar tank equals 468 litres (39 x12 = 468); It is this 468 litres that needs a complementary match by the other teammate's dissimilar tank rating.

Therefore 468 litres divided-by the other teammate's 15 litre/bar tank rating equals 31 bar;
So 31 bar delta from 102 bar usable equals an actual turn pressure SPG reading of 71 bar with regards to the 15 litre/bar tank.

 
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